DRNonHomogeneousTreeLikelihood.cpp

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// SPDX-FileCopyrightText: The Bio++ Development Group
//
// SPDX-License-Identifier: CECILL-2.1
 
#include <Bpp/App/ApplicationTools.h>
#include <Bpp/Text/TextTools.h>
 
#include "../../PatternTools.h"
#include "DRNonHomogeneousTreeLikelihood.h"
 
// From bpp-seq:
#include <Bpp/Seq/SiteTools.h>
#include <Bpp/Seq/Container/AlignedSequenceContainer.h>
#include <Bpp/Seq/Container/SequenceContainerTools.h>
 
using namespace bpp;
 
// From the STL:
#include <iostream>
 
using namespace std;
 
/******************************************************************************/
 
DRNonHomogeneousTreeLikelihood::DRNonHomogeneousTreeLikelihood(
    const Tree& tree,
    std::shared_ptr<SubstitutionModelSet> modelSet,
    std::shared_ptr<DiscreteDistributionInterface> rDist,
    bool verbose,
    bool reparametrizeRoot) :
  AbstractNonHomogeneousTreeLikelihood(tree, modelSet, rDist, verbose, reparametrizeRoot),
  likelihoodData_(),
  minusLogLik_(-1.)
{
  if (!modelSet->isFullySetUpFor(tree))
    throw Exception("DRNonHomogeneousTreeLikelihood(constructor). Model set is not fully specified.");
  init_();
}
 
/******************************************************************************/
 
DRNonHomogeneousTreeLikelihood::DRNonHomogeneousTreeLikelihood(
    const Tree& tree,
    const AlignmentDataInterface& data,
    std::shared_ptr<SubstitutionModelSet> modelSet,
    std::shared_ptr<DiscreteDistributionInterface> rDist,
    bool verbose,
    bool reparametrizeRoot) :
  AbstractNonHomogeneousTreeLikelihood(tree, modelSet, rDist, verbose, reparametrizeRoot),
  likelihoodData_(),
  minusLogLik_(-1.)
{
  if (!modelSet->isFullySetUpFor(tree))
    throw Exception("DRNonHomogeneousTreeLikelihood(constructor). Model set is not fully specified.");
  init_();
  setData(data);
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::init_()
{
  likelihoodData_ = make_unique<DRASDRTreeLikelihoodData>(
        tree_,
        rateDistribution_->getNumberOfCategories());
}
 
/******************************************************************************/
 
DRNonHomogeneousTreeLikelihood::DRNonHomogeneousTreeLikelihood(const DRNonHomogeneousTreeLikelihood& lik) :
  AbstractNonHomogeneousTreeLikelihood(lik),
  likelihoodData_(),
  minusLogLik_(lik.minusLogLik_)
{
  likelihoodData_ = unique_ptr<DRASDRTreeLikelihoodData>(lik.likelihoodData_->clone());
  likelihoodData_->setTree(tree_);
}
 
/******************************************************************************/
 
DRNonHomogeneousTreeLikelihood& DRNonHomogeneousTreeLikelihood::operator=(const DRNonHomogeneousTreeLikelihood& lik)
{
  AbstractNonHomogeneousTreeLikelihood::operator=(lik);
  likelihoodData_ = unique_ptr<DRASDRTreeLikelihoodData>(lik.likelihoodData_->clone());
  likelihoodData_->setTree(tree_);
  minusLogLik_ = lik.minusLogLik_;
  return *this;
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::setData(const AlignmentDataInterface& sites)
{
  data_ = PatternTools::getSequenceSubset(sites, *tree_->getRootNode());
  if (verbose_)
    ApplicationTools::displayTask("Initializing data structure");
  likelihoodData_->initLikelihoods(*data_, *modelSet_->getModel(0)); // We assume here that all models have the same number of states, and that they have the same 'init' method,
                                                                     // Which is a reasonable assumption as long as they share the same alphabet.
  if (verbose_)
    ApplicationTools::displayTaskDone();
 
  nbSites_         = likelihoodData_->getNumberOfSites();
  nbDistinctSites_ = likelihoodData_->getNumberOfDistinctSites();
  nbStates_        = likelihoodData_->getNumberOfStates();
 
  if (verbose_)
    ApplicationTools::displayResult("Number of distinct sites",
        TextTools::toString(nbDistinctSites_));
  initialized_ = false;
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLikelihood() const
{
  double l = 1.;
  Vdouble* lik = &likelihoodData_->getRootRateSiteLikelihoodArray();
  const vector<unsigned int>* w = &likelihoodData_->getWeights();
  for (size_t i = 0; i < nbDistinctSites_; i++)
  {
    l *= std::pow((*lik)[i], (int)(*w)[i]);
  }
  return l;
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLogLikelihood() const
{
  double ll = 0;
  Vdouble* lik = &likelihoodData_->getRootRateSiteLikelihoodArray();
  const vector<unsigned int>* w = &likelihoodData_->getWeights();
  vector<double> la(nbDistinctSites_);
  for (size_t i = 0; i < nbDistinctSites_; i++)
  {
    la[i] = (*w)[i] * log((*lik)[i]);
  }
  sort(la.begin(), la.end());
  for (size_t i = nbDistinctSites_; i > 0; i--)
  {
    ll += la[i - 1];
  }
  return ll;
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLikelihoodForASite(size_t site) const
{
  return likelihoodData_->getRootRateSiteLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)];
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLogLikelihoodForASite(size_t site) const
{
  return log(likelihoodData_->getRootRateSiteLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)]);
}
 
/******************************************************************************/
double DRNonHomogeneousTreeLikelihood::getLikelihoodForASiteForARateClass(size_t site, size_t rateClass) const
{
  return likelihoodData_->getRootSiteLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)][rateClass];
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLogLikelihoodForASiteForARateClass(size_t site, size_t rateClass) const
{
  return log(likelihoodData_->getRootSiteLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)][rateClass]);
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLikelihoodForASiteForARateClassForAState(size_t site, size_t rateClass, int state) const
{
  return likelihoodData_->getRootLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)][rateClass][static_cast<size_t>(state)];
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getLogLikelihoodForASiteForARateClassForAState(size_t site, size_t rateClass, int state) const
{
  return log(likelihoodData_->getRootLikelihoodArray()[likelihoodData_->getRootArrayPosition(site)][rateClass][static_cast<size_t>(state)]);
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::setParameters(const ParameterList& parameters)
{
  setParametersValues(parameters);
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::fireParameterChanged(const ParameterList& params)
{
  applyParameters();
 
  if (params.getCommonParametersWith(rateDistribution_->getIndependentParameters()).size() > 0)
  {
    computeAllTransitionProbabilities();
  }
  else
  {
    vector<int> ids;
    vector<string> tmp = params.getCommonParametersWith(modelSet_->getNodeParameters()).getParameterNames();
    for (size_t i = 0; i < tmp.size(); i++)
    {
      vector<int> tmpv = modelSet_->getNodesWithParameter(tmp[i]);
      ids = VectorTools::vectorUnion(ids, tmpv);
    }
    tmp = params.getCommonParametersWith(brLenParameters_).getParameterNames();
    vector<const Node*> nodes;
    for (size_t i = 0; i < ids.size(); i++)
    {
      nodes.push_back(idToNode_[ids[i]]);
    }
    vector<const Node*> tmpv;
    bool test = false;
    for (size_t i = 0; i < tmp.size(); i++)
    {
      if (tmp[i] == "BrLenRoot" || tmp[i] == "RootPosition")
      {
        if (!test)
        {
          tmpv.push_back(tree_->getRootNode()->getSon(0));
          tmpv.push_back(tree_->getRootNode()->getSon(1));
          test = true; // Add only once.
        }
      }
      else
        tmpv.push_back(nodes_[TextTools::to< size_t >(tmp[i].substr(5))]);
    }
    nodes = VectorTools::vectorUnion(nodes, tmpv);
 
    for (size_t i = 0; i < nodes.size(); i++)
    {
      computeTransitionProbabilitiesForNode(nodes[i]);
    }
    rootFreqs_ = modelSet_->getRootFrequencies();
  }
  computeTreeLikelihood();
  if (computeFirstOrderDerivatives_)
  {
    computeTreeDLikelihoods();
  }
  if (computeSecondOrderDerivatives_)
  {
    computeTreeD2Likelihoods();
  }
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getValue() const
{
  if (!isInitialized())
    throw Exception("DRNonHomogeneousTreeLikelihood::getValue(). Instance is not initialized.");
  return -getLogLikelihood();
}
 
/******************************************************************************
 *                           First Order Derivatives                          *
 ******************************************************************************/
void DRNonHomogeneousTreeLikelihood::computeTreeDLikelihoodAtNode(const Node* node)
{
  const Node* father = node->getFather();
  VVVdouble* _likelihoods_father_node = &likelihoodData_->getLikelihoodArray(father->getId(), node->getId());
  Vdouble* _dLikelihoods_node = &likelihoodData_->getDLikelihoodArray(node->getId());
  VVVdouble*  pxy__node = &pxy_[node->getId()];
  VVVdouble* dpxy__node = &dpxy_[node->getId()];
  VVVdouble larray;
  computeLikelihoodAtNode_(father, larray);
  Vdouble* rootLikelihoodsSR = &likelihoodData_->getRootRateSiteLikelihoodArray();
 
  double dLi, dLic, dLicx, numerator, denominator;
  for (size_t i = 0; i < nbDistinctSites_; i++)
  {
    VVdouble* _likelihoods_father_node_i = &(*_likelihoods_father_node)[i];
    VVdouble* larray_i = &larray[i];
    dLi = 0;
    for (size_t c = 0; c < nbClasses_; c++)
    {
      Vdouble* _likelihoods_father_node_i_c = &(*_likelihoods_father_node_i)[c];
      Vdouble* larray_i_c = &(*larray_i)[c];
      VVdouble*  pxy__node_c = &(*pxy__node)[c];
      VVdouble* dpxy__node_c = &(*dpxy__node)[c];
      dLic = 0;
      for (size_t x = 0; x < nbStates_; x++)
      {
        numerator = 0;
        denominator = 0;
        Vdouble*  pxy__node_c_x = &(*pxy__node_c)[x];
        Vdouble* dpxy__node_c_x = &(*dpxy__node_c)[x];
        dLicx = 0;
        for (size_t y = 0; y < nbStates_; y++)
        {
          numerator   += (*dpxy__node_c_x)[y] * (*_likelihoods_father_node_i_c)[y];
          denominator += (*pxy__node_c_x)[y] * (*_likelihoods_father_node_i_c)[y];
        }
        dLicx = denominator == 0. ? 0. : (*larray_i_c)[x] * numerator / denominator;
        dLic += dLicx;
      }
      dLi += rateDistribution_->getProbability(c) * dLic;
    }
    (*_dLikelihoods_node)[i] = dLi / (*rootLikelihoodsSR)[i];
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeTreeDLikelihoods()
{
  for (size_t k = 0; k < nbNodes_; k++)
  {
    computeTreeDLikelihoodAtNode(nodes_[k]);
  }
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getFirstOrderDerivative(const string& variable) const
{
  if (!hasParameter(variable))
    throw ParameterNotFoundException("DRNonHomogeneousTreeLikelihood::getFirstOrderDerivative().", variable);
  if (getRateDistributionParameters().hasParameter(variable))
  {
    throw Exception("Derivatives respective to rate distribution parameters are not implemented.");
  }
  if (getSubstitutionModelParameters().hasParameter(variable))
  {
    throw Exception("Derivatives respective to substitution model parameters are not implemented.");
  }
 
  //
  // Computation for branch lengths:
  //
  const vector<unsigned int>* w = &likelihoodData_->getWeights();
  Vdouble* _dLikelihoods_branch;
  if (variable == "BrLenRoot")
  {
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(root1_);
    double d1 = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d1 -= (*w)[i] * (*_dLikelihoods_branch)[i];
    }
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(root2_);
    double d2 = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d2 -= (*w)[i] * (*_dLikelihoods_branch)[i];
    }
    double pos = getParameterValue("RootPosition");
    return pos * d1 + (1. - pos) * d2;
  }
  else if (variable == "RootPosition")
  {
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(root1_);
    double d1 = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d1 -= (*w)[i] * (*_dLikelihoods_branch)[i];
    }
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(root2_);
    double d2 = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d2 -= (*w)[i] * (*_dLikelihoods_branch)[i];
    }
    double len = getParameterValue("BrLenRoot");
    return len * (d1 - d2);
  }
  else
  {
    // Get the node with the branch whose length must be derivated:
    size_t brI = TextTools::to<size_t>(variable.substr(5));
    const Node* branch = nodes_[brI];
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(branch->getId());
    double d = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d += (*w)[i] * (*_dLikelihoods_branch)[i];
    }
    return -d;
  }
}
 
/******************************************************************************
 *                           Second Order Derivatives                         *
 ******************************************************************************/
void DRNonHomogeneousTreeLikelihood::computeTreeD2LikelihoodAtNode(const Node* node)
{
  const Node* father = node->getFather();
  VVVdouble* _likelihoods_father_node = &likelihoodData_->getLikelihoodArray(father->getId(), node->getId());
  Vdouble* _d2Likelihoods_node = &likelihoodData_->getD2LikelihoodArray(node->getId());
  VVVdouble*   pxy__node = &pxy_[node->getId()];
  VVVdouble* d2pxy__node = &d2pxy_[node->getId()];
  VVVdouble larray;
  computeLikelihoodAtNode_(father, larray);
  Vdouble* rootLikelihoodsSR = &likelihoodData_->getRootRateSiteLikelihoodArray();
 
  double d2Li, d2Lic, d2Licx, numerator, denominator;
 
  for (size_t i = 0; i < nbDistinctSites_; i++)
  {
    VVdouble* _likelihoods_father_node_i = &(*_likelihoods_father_node)[i];
    VVdouble* larray_i = &larray[i];
    d2Li = 0;
    for (size_t c = 0; c < nbClasses_; c++)
    {
      Vdouble* _likelihoods_father_node_i_c = &(*_likelihoods_father_node_i)[c];
      Vdouble* larray_i_c = &(*larray_i)[c];
      VVdouble*   pxy__node_c = &(*pxy__node)[c];
      VVdouble* d2pxy__node_c = &(*d2pxy__node)[c];
      d2Lic = 0;
      for (size_t x = 0; x < nbStates_; x++)
      {
        numerator = 0;
        denominator = 0;
        Vdouble*   pxy__node_c_x = &(*pxy__node_c)[x];
        Vdouble* d2pxy__node_c_x = &(*d2pxy__node_c)[x];
        d2Licx = 0;
        for (size_t y = 0; y < nbStates_; y++)
        {
          numerator   += (*d2pxy__node_c_x)[y] * (*_likelihoods_father_node_i_c)[y];
          denominator += (*pxy__node_c_x)[y] * (*_likelihoods_father_node_i_c)[y];
        }
        d2Licx = denominator == 0. ? 0. : (*larray_i_c)[x] * numerator / denominator;
        d2Lic += d2Licx;
      }
      d2Li += rateDistribution_->getProbability(c) * d2Lic;
    }
    (*_d2Likelihoods_node)[i] = d2Li / (*rootLikelihoodsSR)[i];
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeTreeD2Likelihoods()
{
  for (size_t k = 0; k < nbNodes_; k++)
  {
    computeTreeD2LikelihoodAtNode(nodes_[k]);
  }
}
 
/******************************************************************************/
 
double DRNonHomogeneousTreeLikelihood::getSecondOrderDerivative(const string& variable) const
{
  if (!hasParameter(variable))
    throw ParameterNotFoundException("DRNonHomogeneousTreeLikelihood::getSecondOrderDerivative().", variable);
  if (getRateDistributionParameters().hasParameter(variable))
  {
    throw Exception("Derivatives respective to rate distribution parameters are not implemented.");
  }
  if (getSubstitutionModelParameters().hasParameter(variable))
  {
    throw Exception("Derivatives respective to substitution model parameters are not implemented.");
  }
 
  //
  // Computation for branch lengths:
  //
 
  const vector<unsigned int>* w = &likelihoodData_->getWeights();
  // We can't deduce second order derivatives regarding BrLenRoot and RootPosition from the
  // branch length derivatives. We need a bit more calculations...
  // NB: we could save a few calculations here...
  if (variable == "BrLenRoot")
  {
    const Node* father = tree_->getRootNode();
 
    // Compute dLikelihoods array for the father node.
    // Fist initialize to 1:
    VVVdouble dLikelihoods_father(nbDistinctSites_);
    VVVdouble d2Likelihoods_father(nbDistinctSites_);
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
      VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
      dLikelihoods_father_i->resize(nbClasses_);
      d2Likelihoods_father_i->resize(nbClasses_);
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
        Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
        dLikelihoods_father_i_c->resize(nbStates_);
        d2Likelihoods_father_i_c->resize(nbStates_);
        for (size_t s = 0; s < nbStates_; s++)
        {
          (*dLikelihoods_father_i_c)[s] = 1.;
          (*d2Likelihoods_father_i_c)[s] = 1.;
        }
      }
    }
 
    size_t nbNodes = father->getNumberOfSons();
    for (size_t l = 0; l < nbNodes; l++)
    {
      const Node* son = father->getSon(l);
 
      if (son->getId() == root1_)
      {
        VVVdouble* _likelihoodsroot1_ = &likelihoodData_->getLikelihoodArray(father->getId(), root1_);
        VVVdouble* _likelihoodsroot2_ = &likelihoodData_->getLikelihoodArray(father->getId(), root2_);
        double pos = getParameterValue("RootPosition");
 
        VVVdouble* d2pxy_root1_ = &d2pxy_[root1_];
        VVVdouble* d2pxy_root2_ = &d2pxy_[root2_];
        VVVdouble* dpxy_root1_  = &dpxy_[root1_];
        VVVdouble* dpxy_root2_  = &dpxy_[root2_];
        VVVdouble* pxy_root1_   = &pxy_[root1_];
        VVVdouble* pxy_root2_   = &pxy_[root2_];
        for (size_t i = 0; i < nbDistinctSites_; i++)
        {
          VVdouble* _likelihoodsroot1__i = &(*_likelihoodsroot1_)[i];
          VVdouble* _likelihoodsroot2__i = &(*_likelihoodsroot2_)[i];
          VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
          VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
          for (size_t c = 0; c < nbClasses_; c++)
          {
            Vdouble* _likelihoodsroot1__i_c = &(*_likelihoodsroot1__i)[c];
            Vdouble* _likelihoodsroot2__i_c = &(*_likelihoodsroot2__i)[c];
            Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
            Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
            VVdouble* d2pxy_root1__c = &(*d2pxy_root1_)[c];
            VVdouble* d2pxy_root2__c = &(*d2pxy_root2_)[c];
            VVdouble* dpxy_root1__c  = &(*dpxy_root1_)[c];
            VVdouble* dpxy_root2__c  = &(*dpxy_root2_)[c];
            VVdouble* pxy_root1__c   = &(*pxy_root1_)[c];
            VVdouble* pxy_root2__c   = &(*pxy_root2_)[c];
            for (size_t x = 0; x < nbStates_; x++)
            {
              Vdouble* d2pxy_root1__c_x = &(*d2pxy_root1__c)[x];
              Vdouble* d2pxy_root2__c_x = &(*d2pxy_root2__c)[x];
              Vdouble* dpxy_root1__c_x  = &(*dpxy_root1__c)[x];
              Vdouble* dpxy_root2__c_x  = &(*dpxy_root2__c)[x];
              Vdouble* pxy_root1__c_x   = &(*pxy_root1__c)[x];
              Vdouble* pxy_root2__c_x   = &(*pxy_root2__c)[x];
              double d2l1 = 0, d2l2 = 0, dl1 = 0, dl2 = 0, l1 = 0, l2 = 0;
              for (size_t y = 0; y < nbStates_; y++)
              {
                d2l1 += (*d2pxy_root1__c_x)[y] * (*_likelihoodsroot1__i_c)[y];
                d2l2 += (*d2pxy_root2__c_x)[y] * (*_likelihoodsroot2__i_c)[y];
                dl1  += (*dpxy_root1__c_x)[y]  * (*_likelihoodsroot1__i_c)[y];
                dl2  += (*dpxy_root2__c_x)[y]  * (*_likelihoodsroot2__i_c)[y];
                l1   += (*pxy_root1__c_x)[y]   * (*_likelihoodsroot1__i_c)[y];
                l2   += (*pxy_root2__c_x)[y]   * (*_likelihoodsroot2__i_c)[y];
              }
              double dl = pos * dl1 * l2 + (1. - pos) * dl2 * l1;
              double d2l = pos * pos * d2l1 * l2 + (1. - pos) * (1. - pos) * d2l2 * l1 + 2 * pos * (1. - pos) * dl1 * dl2;
              (*dLikelihoods_father_i_c)[x] *= dl;
              (*d2Likelihoods_father_i_c)[x] *= d2l;
            }
          }
        }
      }
      else if (son->getId() == root2_)
      {
        // Do nothing, this was accounted when dealing with root1_
      }
      else
      {
        // Account for a putative multifurcation:
        VVVdouble* _likelihoods_son = &likelihoodData_->getLikelihoodArray(father->getId(), son->getId());
 
        VVVdouble* pxy__son = &pxy_[son->getId()];
        for (size_t i = 0; i < nbDistinctSites_; i++)
        {
          VVdouble* _likelihoods_son_i = &(*_likelihoods_son)[i];
          VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
          VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
          for (size_t c = 0; c < nbClasses_; c++)
          {
            Vdouble* _likelihoods_son_i_c = &(*_likelihoods_son_i)[c];
            Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
            Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
            VVdouble* pxy__son_c = &(*pxy__son)[c];
            for (size_t x = 0; x < nbStates_; x++)
            {
              double dl = 0;
              Vdouble* pxy__son_c_x = &(*pxy__son_c)[x];
              for (size_t y = 0; y < nbStates_; y++)
              {
                dl += (*pxy__son_c_x)[y] * (*_likelihoods_son_i_c)[y];
              }
              (*dLikelihoods_father_i_c)[x] *= dl;
              (*d2Likelihoods_father_i_c)[x] *= dl;
            }
          }
        }
      }
    }
    Vdouble* rootLikelihoodsSR = &likelihoodData_->getRootRateSiteLikelihoodArray();
    double d2l = 0, dlx, d2lx;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
      VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
      dlx = 0, d2lx = 0;
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
        Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
        for (size_t x = 0; x < nbStates_; x++)
        {
          dlx += rateDistribution_->getProbability(c) * rootFreqs_[x] * (*dLikelihoods_father_i_c)[x];
          d2lx += rateDistribution_->getProbability(c) * rootFreqs_[x] * (*d2Likelihoods_father_i_c)[x];
        }
      }
      d2l += (*w)[i] * (d2lx / (*rootLikelihoodsSR)[i] - pow(dlx / (*rootLikelihoodsSR)[i], 2));
    }
    return -d2l;
  }
  else if (variable == "RootPosition")
  {
    const Node* father = tree_->getRootNode();
 
    // Compute dLikelihoods array for the father node.
    // Fist initialize to 1:
    VVVdouble dLikelihoods_father(nbDistinctSites_);
    VVVdouble d2Likelihoods_father(nbDistinctSites_);
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
      VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
      dLikelihoods_father_i->resize(nbClasses_);
      d2Likelihoods_father_i->resize(nbClasses_);
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
        Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
        dLikelihoods_father_i_c->resize(nbStates_);
        d2Likelihoods_father_i_c->resize(nbStates_);
        for (size_t s = 0; s < nbStates_; s++)
        {
          (*dLikelihoods_father_i_c)[s] = 1.;
          (*d2Likelihoods_father_i_c)[s] = 1.;
        }
      }
    }
 
    size_t nbNodes = father->getNumberOfSons();
    for (size_t l = 0; l < nbNodes; l++)
    {
      const Node* son = father->getSon(l);
 
      if (son->getId() == root1_)
      {
        VVVdouble* _likelihoodsroot1_ = &likelihoodData_->getLikelihoodArray(father->getId(), root1_);
        VVVdouble* _likelihoodsroot2_ = &likelihoodData_->getLikelihoodArray(father->getId(), root2_);
        double len = getParameterValue("BrLenRoot");
 
        VVVdouble* d2pxy_root1_ = &d2pxy_[root1_];
        VVVdouble* d2pxy_root2_ = &d2pxy_[root2_];
        VVVdouble* dpxy_root1_  = &dpxy_[root1_];
        VVVdouble* dpxy_root2_  = &dpxy_[root2_];
        VVVdouble* pxy_root1_   = &pxy_[root1_];
        VVVdouble* pxy_root2_   = &pxy_[root2_];
        for (size_t i = 0; i < nbDistinctSites_; i++)
        {
          VVdouble* _likelihoodsroot1__i = &(*_likelihoodsroot1_)[i];
          VVdouble* _likelihoodsroot2__i = &(*_likelihoodsroot2_)[i];
          VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
          VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
          for (size_t c = 0; c < nbClasses_; c++)
          {
            Vdouble* _likelihoodsroot1__i_c = &(*_likelihoodsroot1__i)[c];
            Vdouble* _likelihoodsroot2__i_c = &(*_likelihoodsroot2__i)[c];
            Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
            Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
            VVdouble* d2pxy_root1__c = &(*d2pxy_root1_)[c];
            VVdouble* d2pxy_root2__c = &(*d2pxy_root2_)[c];
            VVdouble* dpxy_root1__c  = &(*dpxy_root1_)[c];
            VVdouble* dpxy_root2__c  = &(*dpxy_root2_)[c];
            VVdouble* pxy_root1__c   = &(*pxy_root1_)[c];
            VVdouble* pxy_root2__c   = &(*pxy_root2_)[c];
            for (size_t x = 0; x < nbStates_; x++)
            {
              Vdouble* d2pxy_root1__c_x = &(*d2pxy_root1__c)[x];
              Vdouble* d2pxy_root2__c_x = &(*d2pxy_root2__c)[x];
              Vdouble* dpxy_root1__c_x  = &(*dpxy_root1__c)[x];
              Vdouble* dpxy_root2__c_x  = &(*dpxy_root2__c)[x];
              Vdouble* pxy_root1__c_x   = &(*pxy_root1__c)[x];
              Vdouble* pxy_root2__c_x   = &(*pxy_root2__c)[x];
              double d2l1 = 0, d2l2 = 0, dl1 = 0, dl2 = 0, l1 = 0, l2 = 0;
              for (size_t y = 0; y < nbStates_; y++)
              {
                d2l1 += (*d2pxy_root1__c_x)[y] * (*_likelihoodsroot1__i_c)[y];
                d2l2 += (*d2pxy_root2__c_x)[y] * (*_likelihoodsroot2__i_c)[y];
                dl1  += (*dpxy_root1__c_x)[y]  * (*_likelihoodsroot1__i_c)[y];
                dl2  += (*dpxy_root2__c_x)[y]  * (*_likelihoodsroot2__i_c)[y];
                l1   += (*pxy_root1__c_x)[y]   * (*_likelihoodsroot1__i_c)[y];
                l2   += (*pxy_root2__c_x)[y]   * (*_likelihoodsroot2__i_c)[y];
              }
              double dl = len * (dl1 * l2 - dl2 * l1);
              double d2l = len * len * (d2l1 * l2 + d2l2 * l1 - 2 * dl1 * dl2);
              (*dLikelihoods_father_i_c)[x] *= dl;
              (*d2Likelihoods_father_i_c)[x] *= d2l;
            }
          }
        }
      }
      else if (son->getId() == root2_)
      {
        // Do nothing, this was accounted when dealing with root1_
      }
      else
      {
        // Account for a putative multifurcation:
        VVVdouble* _likelihoods_son = &likelihoodData_->getLikelihoodArray(father->getId(), son->getId());
 
        VVVdouble* pxy__son = &pxy_[son->getId()];
        for (size_t i = 0; i < nbDistinctSites_; i++)
        {
          VVdouble* _likelihoods_son_i = &(*_likelihoods_son)[i];
          VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
          VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
          for (size_t c = 0; c < nbClasses_; c++)
          {
            Vdouble* _likelihoods_son_i_c = &(*_likelihoods_son_i)[c];
            Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
            Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
            VVdouble* pxy__son_c = &(*pxy__son)[c];
            for (size_t x = 0; x < nbStates_; x++)
            {
              double dl = 0;
              Vdouble* pxy__son_c_x = &(*pxy__son_c)[x];
              for (size_t y = 0; y < nbStates_; y++)
              {
                dl += (*pxy__son_c_x)[y] * (*_likelihoods_son_i_c)[y];
              }
              (*dLikelihoods_father_i_c)[x] *= dl;
              (*d2Likelihoods_father_i_c)[x] *= dl;
            }
          }
        }
      }
    }
    Vdouble* rootLikelihoodsSR = &likelihoodData_->getRootRateSiteLikelihoodArray();
    double d2l = 0, dlx, d2lx;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* dLikelihoods_father_i = &dLikelihoods_father[i];
      VVdouble* d2Likelihoods_father_i = &d2Likelihoods_father[i];
      dlx = 0, d2lx = 0;
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* dLikelihoods_father_i_c = &(*dLikelihoods_father_i)[c];
        Vdouble* d2Likelihoods_father_i_c = &(*d2Likelihoods_father_i)[c];
        for (size_t x = 0; x < nbStates_; x++)
        {
          dlx += rateDistribution_->getProbability(c) * rootFreqs_[x] * (*dLikelihoods_father_i_c)[x];
          d2lx += rateDistribution_->getProbability(c) * rootFreqs_[x] * (*d2Likelihoods_father_i_c)[x];
        }
      }
      d2l += (*w)[i] * (d2lx / (*rootLikelihoodsSR)[i] - pow(dlx / (*rootLikelihoodsSR)[i], 2));
    }
    return -d2l;
  }
  else
  {
    Vdouble* _dLikelihoods_branch;
    Vdouble* _d2Likelihoods_branch;
    // Get the node with the branch whose length must be derivated:
    size_t brI = TextTools::to<size_t>(variable.substr(5));
    const Node* branch = nodes_[brI];
    _dLikelihoods_branch = &likelihoodData_->getDLikelihoodArray(branch->getId());
    _d2Likelihoods_branch = &likelihoodData_->getD2LikelihoodArray(branch->getId());
    double d2l = 0;
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      d2l += (*w)[i] * ((*_d2Likelihoods_branch)[i] - pow((*_dLikelihoods_branch)[i], 2));
    }
    return -d2l;
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::resetLikelihoodArrays(const Node* node)
{
  for (size_t n = 0; n < node->getNumberOfSons(); n++)
  {
    const Node* subNode = node->getSon(n);
    resetLikelihoodArray(likelihoodData_->getLikelihoodArray(node->getId(), subNode->getId()));
  }
  if (node->hasFather())
  {
    const Node* father = node->getFather();
    resetLikelihoodArray(likelihoodData_->getLikelihoodArray(node->getId(), father->getId()));
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeTreeLikelihood()
{
  computeSubtreeLikelihoodPostfix(tree_->getRootNode());
  computeSubtreeLikelihoodPrefix(tree_->getRootNode());
  computeRootLikelihood();
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeSubtreeLikelihoodPostfix(const Node* node)
{
  //  if(node->isLeaf()) return;
  // cout << node->getId() << "\t" << (node->hasName()?node->getName():"") << endl;
  if (node->getNumberOfSons() == 0)
    return;
 
  // Set all likelihood arrays to 1 for a start:
  resetLikelihoodArrays(node);
 
  map<int, VVVdouble>* _likelihoods_node = &likelihoodData_->getLikelihoodArrays(node->getId());
  size_t nbNodes = node->getNumberOfSons();
  for (size_t l = 0; l < nbNodes; l++)
  {
    // For each son node...
 
    const Node* son = node->getSon(l);
    VVVdouble* _likelihoods_node_son = &(*_likelihoods_node)[son->getId()];
 
    if (son->isLeaf())
    {
      VVdouble* _likelihoods_leaf = &likelihoodData_->getLeafLikelihoods(son->getId());
      for (size_t i = 0; i < nbDistinctSites_; i++)
      {
        // For each site in the sequence,
        Vdouble* _likelihoods_leaf_i = &(*_likelihoods_leaf)[i];
        VVdouble* _likelihoods_node_son_i = &(*_likelihoods_node_son)[i];
        for (size_t c = 0; c < nbClasses_; c++)
        {
          // For each rate class,
          Vdouble* _likelihoods_node_son_i_c = &(*_likelihoods_node_son_i)[c];
          for (size_t x = 0; x < nbStates_; x++)
          {
            // For each initial state,
            (*_likelihoods_node_son_i_c)[x] = (*_likelihoods_leaf_i)[x];
          }
        }
      }
    }
    else
    {
      computeSubtreeLikelihoodPostfix(son); // Recursive method:
      size_t nbSons = son->getNumberOfSons();
      map<int, VVVdouble>* _likelihoods_son = &likelihoodData_->getLikelihoodArrays(son->getId());
 
      vector<const VVVdouble*> iLik(nbSons);
      vector<const VVVdouble*> tProb(nbSons);
      for (size_t n = 0; n < nbSons; n++)
      {
        const Node* sonSon = son->getSon(n);
        tProb[n] = &pxy_[sonSon->getId()];
        iLik[n] = &(*_likelihoods_son)[sonSon->getId()];
      }
      computeLikelihoodFromArrays(iLik, tProb, *_likelihoods_node_son, nbSons, nbDistinctSites_, nbClasses_, nbStates_, false);
    }
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeSubtreeLikelihoodPrefix(const Node* node)
{
  if (!node->hasFather())
  {
    // 'node' is the root of the tree.
    // Just call the method on each son node:
    size_t nbSons = node->getNumberOfSons();
    for (size_t n = 0; n < nbSons; n++)
    {
      computeSubtreeLikelihoodPrefix(node->getSon(n));
    }
    return;
  }
  else
  {
    const Node* father = node->getFather();
    map<int, VVVdouble>* _likelihoods_node = &likelihoodData_->getLikelihoodArrays(node->getId());
    map<int, VVVdouble>* _likelihoods_father = &likelihoodData_->getLikelihoodArrays(father->getId());
    VVVdouble* _likelihoods_node_father = &(*_likelihoods_node)[father->getId()];
    if (node->isLeaf())
    {
      resetLikelihoodArray(*_likelihoods_node_father);
    }
 
    if (father->isLeaf())
    {
      // If the tree is rooted by a leaf
      VVdouble* _likelihoods_leaf = &likelihoodData_->getLeafLikelihoods(father->getId());
      for (size_t i = 0; i < nbDistinctSites_; i++)
      {
        // For each site in the sequence,
        Vdouble* _likelihoods_leaf_i = &(*_likelihoods_leaf)[i];
        VVdouble* _likelihoods_node_father_i = &(*_likelihoods_node_father)[i];
        for (size_t c = 0; c < nbClasses_; c++)
        {
          // For each rate class,
          Vdouble* _likelihoods_node_father_i_c = &(*_likelihoods_node_father_i)[c];
          for (size_t x = 0; x < nbStates_; x++)
          {
            // For each initial state,
            (*_likelihoods_node_father_i_c)[x] = (*_likelihoods_leaf_i)[x];
          }
        }
      }
    }
    else
    {
      vector<const Node*> nodes;
      // Add brothers:
      size_t nbFatherSons = father->getNumberOfSons();
      for (size_t n = 0; n < nbFatherSons; n++)
      {
        const Node* son = father->getSon(n);
        if (son->getId() != node->getId())
          nodes.push_back(son); // This is a real brother, not current node!
      }
      // Now the real stuff... We've got to compute the likelihoods for the
      // subtree defined by node 'father'.
      // This is the same as postfix method, but with different subnodes.
 
      size_t nbSons = nodes.size(); // In case of a bifurcating tree this is equal to 1.
 
      vector<const VVVdouble*> iLik(nbSons);
      vector<const VVVdouble*> tProb(nbSons);
      for (size_t n = 0; n < nbSons; n++)
      {
        const Node* fatherSon = nodes[n];
        tProb[n] = &pxy_[fatherSon->getId()];
        iLik[n] = &(*_likelihoods_father)[fatherSon->getId()];
      }
 
      if (father->hasFather())
      {
        const Node* fatherFather = father->getFather();
        computeLikelihoodFromArrays(iLik, tProb, &(*_likelihoods_father)[fatherFather->getId()], &pxy_[father->getId()], *_likelihoods_node_father, nbSons, nbDistinctSites_, nbClasses_, nbStates_, false);
      }
      else
      {
        computeLikelihoodFromArrays(iLik, tProb, *_likelihoods_node_father, nbSons, nbDistinctSites_, nbClasses_, nbStates_, false);
      }
    }
 
    if (!father->hasFather())
    {
      // We have to account for the root frequencies:
      for (size_t i = 0; i < nbDistinctSites_; i++)
      {
        VVdouble* _likelihoods_node_father_i = &(*_likelihoods_node_father)[i];
        for (size_t c = 0; c < nbClasses_; c++)
        {
          Vdouble* _likelihoods_node_father_i_c = &(*_likelihoods_node_father_i)[c];
          for (size_t x = 0; x < nbStates_; x++)
          {
            (*_likelihoods_node_father_i_c)[x] *= rootFreqs_[x];
          }
        }
      }
    }
 
    // Call the method on each son node:
    size_t nbNodeSons = node->getNumberOfSons();
    for (size_t i = 0; i < nbNodeSons; i++)
    {
      computeSubtreeLikelihoodPrefix(node->getSon(i)); // Recursive method.
    }
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeRootLikelihood()
{
  const Node* root = tree_->getRootNode();
  VVVdouble* rootLikelihoods = &likelihoodData_->getRootLikelihoodArray();
  // Set all likelihoods to 1 for a start:
  if (root->isLeaf())
  {
    VVdouble* leavesLikelihoods_root = &likelihoodData_->getLeafLikelihoods(root->getId());
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* rootLikelihoods_i = &(*rootLikelihoods)[i];
      Vdouble* leavesLikelihoods_root_i = &(*leavesLikelihoods_root)[i];
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* rootLikelihoods_i_c = &(*rootLikelihoods_i)[c];
        for (size_t x = 0; x < nbStates_; x++)
        {
          (*rootLikelihoods_i_c)[x] = (*leavesLikelihoods_root_i)[x];
        }
      }
    }
  }
  else
  {
    resetLikelihoodArray(*rootLikelihoods);
  }
 
  map<int, VVVdouble>* likelihoods_root = &likelihoodData_->getLikelihoodArrays(root->getId());
  size_t nbNodes = root->getNumberOfSons();
  vector<const VVVdouble*> iLik(nbNodes);
  vector<const VVVdouble*> tProb(nbNodes);
  for (size_t n = 0; n < nbNodes; n++)
  {
    const Node* son = root->getSon(n);
    tProb[n] = &pxy_[son->getId()];
    iLik[n] = &(*likelihoods_root)[son->getId()];
  }
  computeLikelihoodFromArrays(iLik, tProb, *rootLikelihoods, nbNodes, nbDistinctSites_, nbClasses_, nbStates_, false);
 
  Vdouble p = rateDistribution_->getProbabilities();
  VVdouble* rootLikelihoodsS  = &likelihoodData_->getRootSiteLikelihoodArray();
  Vdouble* rootLikelihoodsSR = &likelihoodData_->getRootRateSiteLikelihoodArray();
  for (size_t i = 0; i < nbDistinctSites_; i++)
  {
    // For each site in the sequence,
    VVdouble* rootLikelihoods_i = &(*rootLikelihoods)[i];
    Vdouble* rootLikelihoodsS_i = &(*rootLikelihoodsS)[i];
    (*rootLikelihoodsSR)[i] = 0;
    for (size_t c = 0; c < nbClasses_; c++)
    {
      // For each rate class,
      Vdouble* rootLikelihoods_i_c = &(*rootLikelihoods_i)[c];
      double* rootLikelihoodsS_i_c = &(*rootLikelihoodsS_i)[c];
      (*rootLikelihoodsS_i_c) = 0;
      for (size_t x = 0; x < nbStates_; x++)
      {
        // For each initial state,
        (*rootLikelihoodsS_i_c) += rootFreqs_[x] * (*rootLikelihoods_i_c)[x];
      }
      (*rootLikelihoodsSR)[i] += p[c] * (*rootLikelihoodsS_i_c);
    }
 
    // Final checking (for numerical errors):
    if ((*rootLikelihoodsSR)[i] < 0)
      (*rootLikelihoodsSR)[i] = 0.;
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeLikelihoodAtNode_(const Node* node, VVVdouble& likelihoodArray) const
{
  //  const Node * node = tree_->getNode(nodeId);
  int nodeId = node->getId();
  likelihoodArray.resize(nbDistinctSites_);
  map<int, VVVdouble>* likelihoods_node = &likelihoodData_->getLikelihoodArrays(node->getId());
 
  // Initialize likelihood array:
  if (node->isLeaf())
  {
    VVdouble* leavesLikelihoods_node = &likelihoodData_->getLeafLikelihoods(nodeId);
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* likelihoodArray_i = &likelihoodArray[i];
      Vdouble* leavesLikelihoods_node_i = &(*leavesLikelihoods_node)[i];
      likelihoodArray_i->resize(nbClasses_);
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* likelihoodArray_i_c = &(*likelihoodArray_i)[c];
        likelihoodArray_i_c->resize(nbStates_);
        for (size_t x = 0; x < nbStates_; x++)
        {
          (*likelihoodArray_i_c)[x] = (*leavesLikelihoods_node_i)[x];
        }
      }
    }
  }
  else
  {
    // Otherwise:
    // Set all likelihoods to 1 for a start:
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* likelihoodArray_i = &likelihoodArray[i];
      likelihoodArray_i->resize(nbClasses_);
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* likelihoodArray_i_c = &(*likelihoodArray_i)[c];
        likelihoodArray_i_c->resize(nbStates_);
        for (size_t x = 0; x < nbStates_; x++)
        {
          (*likelihoodArray_i_c)[x] = 1.;
        }
      }
    }
  }
 
  size_t nbNodes = node->getNumberOfSons();
 
  vector<const VVVdouble*> iLik(nbNodes);
  vector<const VVVdouble*> tProb(nbNodes);
  for (size_t n = 0; n < nbNodes; n++)
  {
    const Node* son = node->getSon(n);
    tProb[n] = &pxy_[son->getId()];
    iLik[n] = &(*likelihoods_node)[son->getId()];
  }
 
  if (node->hasFather())
  {
    const Node* father = node->getFather();
    computeLikelihoodFromArrays(iLik, tProb, &(*likelihoods_node)[father->getId()], &pxy_[nodeId], likelihoodArray, nbNodes, nbDistinctSites_, nbClasses_, nbStates_, false);
  }
  else
  {
    computeLikelihoodFromArrays(iLik, tProb, likelihoodArray, nbNodes, nbDistinctSites_, nbClasses_, nbStates_, false);
 
    // We have to account for the root frequencies:
    for (size_t i = 0; i < nbDistinctSites_; i++)
    {
      VVdouble* likelihoodArray_i = &likelihoodArray[i];
      for (size_t c = 0; c < nbClasses_; c++)
      {
        Vdouble* likelihoodArray_i_c = &(*likelihoodArray_i)[c];
        for (size_t x = 0; x < nbStates_; x++)
        {
          (*likelihoodArray_i_c)[x] *= rootFreqs_[x];
        }
      }
    }
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeLikelihoodFromArrays(
    const vector<const VVVdouble*>& iLik,
    const vector<const VVVdouble*>& tProb,
    VVVdouble& oLik,
    size_t nbNodes,
    size_t nbDistinctSites,
    size_t nbClasses,
    size_t nbStates,
    bool reset)
{
  if (reset)
    resetLikelihoodArray(oLik);
 
  for (size_t n = 0; n < nbNodes; n++)
  {
    const VVVdouble* pxy_n = tProb[n];
    const VVVdouble* iLik_n = iLik[n];
 
    for (size_t i = 0; i < nbDistinctSites; i++)
    {
      // For each site in the sequence,
      const VVdouble* iLik_n_i = &(*iLik_n)[i];
      VVdouble* oLik_i = &(oLik)[i];
 
      for (size_t c = 0; c < nbClasses; c++)
      {
        // For each rate class,
        const Vdouble* iLik_n_i_c = &(*iLik_n_i)[c];
        Vdouble* oLik_i_c = &(*oLik_i)[c];
        const VVdouble* pxy_n_c = &(*pxy_n)[c];
        for (size_t x = 0; x < nbStates; x++)
        {
          // For each initial state,
          const Vdouble* pxy_n_c_x = &(*pxy_n_c)[x];
          double likelihood = 0;
          for (size_t y = 0; y < nbStates; y++)
          {
            likelihood += (*pxy_n_c_x)[y] * (*iLik_n_i_c)[y];
          }
          // We store this conditional likelihood into the corresponding array:
          (*oLik_i_c)[x] *= likelihood;
        }
      }
    }
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::computeLikelihoodFromArrays(
    const vector<const VVVdouble*>& iLik,
    const vector<const VVVdouble*>& tProb,
    const VVVdouble* iLikR,
    const VVVdouble* tProbR,
    VVVdouble& oLik,
    size_t nbNodes,
    size_t nbDistinctSites,
    size_t nbClasses,
    size_t nbStates,
    bool reset)
{
  if (reset)
    resetLikelihoodArray(oLik);
 
  for (size_t n = 0; n < nbNodes; n++)
  {
    const VVVdouble* pxy_n = tProb[n];
    const VVVdouble* iLik_n = iLik[n];
 
    for (size_t i = 0; i < nbDistinctSites; i++)
    {
      // For each site in the sequence,
      const VVdouble* iLik_n_i = &(*iLik_n)[i];
      VVdouble* oLik_i = &(oLik)[i];
 
      for (size_t c = 0; c < nbClasses; c++)
      {
        // For each rate class,
        const Vdouble* iLik_n_i_c = &(*iLik_n_i)[c];
        Vdouble* oLik_i_c = &(*oLik_i)[c];
        const VVdouble* pxy_n_c = &(*pxy_n)[c];
        for (size_t x = 0; x < nbStates; x++)
        {
          // For each initial state,
          const Vdouble* pxy_n_c_x = &(*pxy_n_c)[x];
          double likelihood = 0;
          for (size_t y = 0; y < nbStates; y++)
          {
            // cout << "1:" << (* pxy_n_c_x)[y]  << endl;
            // cout << "2:" << (* iLik_n_i_c)[y] << endl;
            likelihood += (*pxy_n_c_x)[y] * (*iLik_n_i_c)[y];
            // cout << i << "\t" << c << "\t" << x << "\t" << y << "\t" <<  (* pxy__son_c_x)[y] << "\t" << (* likelihoods_root_son_i_c)[y] << endl;
          }
          // We store this conditional likelihood into the corresponding array:
          (*oLik_i_c)[x] *= likelihood;
        }
      }
    }
  }
 
  // Now deal with the subtree containing the root:
  for (size_t i = 0; i < nbDistinctSites; i++)
  {
    // For each site in the sequence,
    const VVdouble* iLikR_i = &(*iLikR)[i];
    VVdouble* oLik_i = &(oLik)[i];
 
    for (size_t c = 0; c < nbClasses; c++)
    {
      // For each rate class,
      const Vdouble* iLikR_i_c = &(*iLikR_i)[c];
      Vdouble* oLik_i_c = &(*oLik_i)[c];
      const VVdouble* pxyR_c = &(*tProbR)[c];
      for (size_t x = 0; x < nbStates; x++)
      {
        double likelihood = 0;
        for (size_t y = 0; y < nbStates; y++)
        {
          // For each final state,
          const Vdouble* pxyR_c_y = &(*pxyR_c)[y];
          likelihood += (*pxyR_c_y)[x] * (*iLikR_i_c)[y];
        }
        // We store this conditional likelihood into the corresponding array:
        (*oLik_i_c)[x] *= likelihood;
      }
    }
  }
}
 
/******************************************************************************/
 
void DRNonHomogeneousTreeLikelihood::displayLikelihood(const Node* node)
{
  cout << "Likelihoods at node " << node->getId() << ": " << endl;
  for (size_t n = 0; n < node->getNumberOfSons(); n++)
  {
    const Node* subNode = node->getSon(n);
    cout << "Array for sub-node " << subNode->getId() << endl;
    displayLikelihoodArray(likelihoodData_->getLikelihoodArray(node->getId(), subNode->getId()));
  }
  if (node->hasFather())
  {
    const Node* father = node->getFather();
    cout << "Array for father node " << father->getId() << endl;
    displayLikelihoodArray(likelihoodData_->getLikelihoodArray(node->getId(), father->getId()));
  }
  cout << "                                         ***" << endl;
}
 
/*******************************************************************************/